Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity
Applications of Mathematics (2011)
- Volume: 56, Issue: 6, page 543-555
- ISSN: 0862-7940
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topYao, Qingliu. "Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity." Applications of Mathematics 56.6 (2011): 543-555. <http://eudml.org/doc/196729>.
@article{Yao2011,
abstract = {We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions \[ \{\left\lbrace \begin\{array\}\{ll\} u^\{(4)\}(t)=f\bigl (t,u(t),u^\{\prime \}(t),u^\{\prime \prime \}(t),u^\{\prime \prime \prime \}(t)\bigr ),\quad \text\{a.e.\} \ t\in [0,1],\\ u(0)=a, \ u^\{\prime \}(0)=b, \ u(1)=c, \ u^\{\prime \prime \}(1)=d, \end\{array\}\right.\} \]
where the nonlinear term $f(t,u_\{0\},u_\{1\},u_\{2\},u_\{3\})$ is a strong Carathéodory function. By constructing suitable height functions of the nonlinear term $f(t,u_\{0\},u_\{1\},u_\{2\},u_\{3\})$ on bounded sets and applying the Leray-Schauder fixed point theorem, we prove that the equation has a solution provided that the integration of some height function has an appropriate value.},
author = {Yao, Qingliu},
journal = {Applications of Mathematics},
keywords = {nonlinear ordinary differential equation; boundary value problem; existence; fixed point theorem; nonlinear ordinary differential equation; boundary value problem; existence; fixed point theorem},
language = {eng},
number = {6},
pages = {543-555},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity},
url = {http://eudml.org/doc/196729},
volume = {56},
year = {2011},
}
TY - JOUR
AU - Yao, Qingliu
TI - Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 6
SP - 543
EP - 555
AB - We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions \[ {\left\lbrace \begin{array}{ll} u^{(4)}(t)=f\bigl (t,u(t),u^{\prime }(t),u^{\prime \prime }(t),u^{\prime \prime \prime }(t)\bigr ),\quad \text{a.e.} \ t\in [0,1],\\ u(0)=a, \ u^{\prime }(0)=b, \ u(1)=c, \ u^{\prime \prime }(1)=d, \end{array}\right.} \]
where the nonlinear term $f(t,u_{0},u_{1},u_{2},u_{3})$ is a strong Carathéodory function. By constructing suitable height functions of the nonlinear term $f(t,u_{0},u_{1},u_{2},u_{3})$ on bounded sets and applying the Leray-Schauder fixed point theorem, we prove that the equation has a solution provided that the integration of some height function has an appropriate value.
LA - eng
KW - nonlinear ordinary differential equation; boundary value problem; existence; fixed point theorem; nonlinear ordinary differential equation; boundary value problem; existence; fixed point theorem
UR - http://eudml.org/doc/196729
ER -
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